Rockfish Historical Harvest Estimates

This project seeks to estimate sport fish harvest and releases of rockfish in Alaska waters by improving on the Howard et al. (2020) methods and expand the time series back to 1977 when the statewide harvest survey (SWHS) was first implemented. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and replaces the Howard decision tree approach to low sample sizes with a hierarchical model. The methods and results for generating harvest estimates are generally consistent between the Bayesian model and the Howard methods. Harvest estimates are consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data.

The Bayesian methods depart from the Howard method in how releases are estimated. The Howard methods assume that the species composition of the harvests are equal to the species composition of released fish, which is clearly contraindicated in the logbook data. For instance, logbook data demonstrates that yelloweye have been retained at high levels up until restrictions were enacted in recent years, whereas pelagic rockfish were released in significant numbers in the past with retention increasing in recent years as they have become more prized by anglers. Recent prohibition on retaining yelloweye in Southeast Alaska highlights the shortcomings of the original Howard assumptions as the species composition of the harvest would indicate that no yelloweye were caught and released during the closure.

The Howard method for estimating releases for private anglers also relied on an expansion of the logbook release estimates based on the ratio of private:guided releases of all rockfish in the SWHS. In addition to the faulty assumptions about species composition, this method ignores potential bias in SWHS estimates of harvests and releases or at least assumes that the bias in release and harvests are the same. As demonstrated in Figure 1, the bias in those two quantities appears to be quite different based on the logbook data. The Bayesian model thus attempts to estimate release probabilities based on the logbook data coupled with bias corrected estimates from the SWHS.

Lastly, the Howard methods were only used on data beginning in 1999 with the advent of the logbook program and estimates of harvests and releases prior to that have been based on linear ramps from 1999 back to the perceived start of the fishery. The Bayesian methods allow us to expand the time series back to 1977 when the SWHS was implemented by leveraging regional data trends in species composition and the proportion of caught rockfish harvested by species and/or species complex. Key advantages of the Bayesian approach are highlighted in table 1.

Table 1. Summary of key improvements in reconstructiing sport fish removals of rockfish using the Bayesian model as compared to the Howard et al. (2020) methods.

Issue	Howard	Bayes
Time series	1999 - present	1977 - present
Bias in SWHS	Not explicitly dealt with. Relies on logbook data and ratios of guided/unguided from SWHS data to estimate unguided releases and harvests.	Explicitly estimates bias in SWHS harvest and release estimates based on logbook data.
Species composition of releases	Assumes that species composition of releases is equal to that of the harvest, which is not evident in the logbook data.	Recognizes different release probabilities by species / species assemblage and estimates it from logbook data and bias corrected SWHS data
Sample size limitations	Uses sample size threshholds such that when areas fall below those threshholds values are borrowed from nearby areas.	Uses a hierarchichacal modelling approach that shares information between areas in the same region. Thus all data is used, even with small sample sizes. This is a more sound method that avoids assumptions and uses all of the data.
Error propogation	Error is propogated when variance estimates are available, but there is uncertainty associated with borrowing values from nearby areas, or the assumption of species compositions being identical in harvest and releases, are not dealt with.	By breaking the assumption that species composition is equal between harvests and releases, uncertainty in the release estimates is more reflective of the fishery. Furthermore, the hyerarchichal approach more accurately captures uncertainy within and between areas within a region.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are overall harvest estimates from 1977- 1995 and release estimates from 1990-1995 that required some partitioning to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied to the pre-1996 values.

Figure 1.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units. Note that initial rockfish harvest estimates were not differentiated into species assemblage or species until 1998 when logbooks began differentiating by pelagic and non-pelagic. Logbooks began to collect data on yelloweye beginning in 2006. Port sampling programs to gather data on species composition of harvests began in 1996 in Southcentral and Kodiak and in 2006 in Southeast.

SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook records are a census of guided harvests and releases.

SWHS Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides have been required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

Figure 2.- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).

A note on model development

To evaluate the discrepancy in apparent bias in harvest and release data, several models were explored to estimate releases during model development. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treated the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases. This tensions eventually highlighted the different release/retention probabilities between yelloweye and pelagics in the logbook data and prompted the current approach whereby that probability was calculated for the three main species complexes covered in the data: pelagics, yelloweye, and “other”. The methods described here follow the (\(LB_{fit}\)) formulation. Based on model behavior it is unlikely that the (\(LB_{cens}\)) model would work as there would not be enough data to estimate release probabilities. However, it may be worth running the (\(LB_{hyb}\)) approach as a sensitivity test at the very least.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish. In Southeast Alaska, the number of Demersal Shelf Rockfish (DSR, of which yelloweye are one species) and slope rockfish are also recorded.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta0_{(comp)ayu} + \frac{\beta1_{(comp)ayu}}{(1 + exp(\beta2_{(comp)ayu}*(y - \beta3_{(comp)ayu})))} + \beta4_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior. \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernible change in composition over the observed time period. \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was used for hindcasting.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested, \(pH_{(comp)ayu}\), by area, year, user group and species grouping. Because release data from the SWHS is for all rockfish and the release data from logbooks is only subdivided into pelagics, yelloweye and “other” (non-pelagic, non-yelloweye), we only estimated \(pH_{(comp)ayu}\) for those categories. Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases. For non-yelloweye DSR and Slope rockfish assemblages in Southeast Alaska \(R_{(DSR)ayu}\) and \(R_{(slope)ayu}\) were estimated from \(R_{(other)ayu}\) using the species composition data from the harvest, thus assuming that slope and DSR assemblages were caught and released at the same rates.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta0_{(pH)ayu} + \frac{\beta1_{(pH)ayuc}}{(1 + exp(\beta2_{(pH)ayuc}*(y - \beta3_{(pH)ayuc})))} + \beta4_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990. As with the compositional trends, \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernable change in harvest probability over the observed time period, \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was applied.

Release mortality (i.e., the number of released rockfish expected to die) was calculated assuming fixed mortality rates developed in each of the regions. Deep water release (DWR) devices were mandated for charter fleets in 2013 and rates were derived from CITATION. Southeast applies basic rates estimated in these studies while Southcentral and Kodiak rates were derived by using historical depth-of-release data to adjust the rates based on area and user group.

The total number of mortalities by year, area, user and species/species assemblage in numbers was calculated by summing harvests and release mortality such that

\[\begin{equation} M_{(comp)ayu}~=~ H_{(comp)ayu} + m_{R-(comp)ayu} * R_{(comp)ayu} \end{equation}\]

where \(m_{R-(comp)ayu}\) is the release mortality rate by year, area, user and species (Figure XX).

Total removals in biomass were converted using the average weight of fish from port sampling?. A minimum sample size per year of X fish was used as the cutoff for including in the data set. Weights were modeled hierarchically to estimate weights in years when data was missing. The total biomass of removals by year, area, user and species was thus

\[\begin{equation} B_{(comp)ayu}~=~ \overline{wt}_{(comp)ayu} * M_{(comp)ayu} \end{equation}\]

where \(\overline{wt}_{(comp)ayu}\) is the mean weight by species, area, user and year.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. As such, the release data are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), a second approaches was considered that loosened the assumption that logbook releases were a census. Methods explored to develope \(LB_{hyb}\) and \(LB_{cens}\) models are detailed at the end of this section.

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs was thus a proportion of the pelagic harvests

\[\begin{equation} x_{(black)ayu}~\sim~\textrm{Binomial}(P_{(black)ayu}, N_{ayu}^{pel}) \end{equation}\]

Yelloweye rockfish in Southcentral and Kodiak were modeled similarly as a proportion of the total number of non-pelagics such that

\[\begin{equation} x_{(yellow_{R2})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R2})ayu}, N_{ayu}^{nonpel}) \end{equation}\]

Southeast areas have several other non-pelagic groupings such that DSR and slope rockfish are a proportion of non-pelagics

\[\begin{equation} x_{(DSR)ayu}~\sim~\textrm{Binomial}(P_{(DSR)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

and

\[\begin{equation} x_{(slope)ayu}~\sim~\textrm{Binomial}(P_{(slope)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

with yelloweye in southeast a proportion of the DSR harvest

\[\begin{equation} x_{(yellow_{R1})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R1})ayu}, N_{ayu}^{DSR}). \end{equation}\].

Kodiak has limited port sampling beyond the main harbors but has a robust hydroacoustic survey that is used to quantify black rockfish abundance across the management area and uses stereocameras to derive species compositions of the hydroacoustic data. This data was used as supplementary data to further inform the model to the proportion of pelagic rockfish that are black in Kodiak areas. Angler landings in Kodiak show a higher proportion of black rockfish relative to the hydroacoustic survey and thus the proportion of black rockfish in the hydroacoustic sample related to the true proportion such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ P_{(black|pelagic)ayu} + ae_{au} \end{equation}\].

where \(ae_{au}\) is the angler effect for each area and user group modeled hierarchically around a mean of 0. Predicted \(P_{(black|pelagic)ayu}^{HA}\) assumed a beta distribution such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ beta(\alpha_{HA},\beta_{HA}) \end{equation}\]

where

\[\begin{equation} \alpha_{HA} ~=~ (P_{(black|pelagic)ayu}^{HA})^2 * \frac{1 - P_{(black|pelagic)ayu}^{HA}}{\frac{var_{P_{HA}}-1}{P_{(black|pelagic)ayu}^{HA}}}, \end{equation}\]

\[\begin{equation} \beta_{HA} ~=~ (\alpha_{HA}) * \frac{1}{P_{(black|pelagic)ayu}^{HA} - 1}, \end{equation}\]

\[\begin{equation} var_{P_{HA}} ~=~ (P_{(black|pelagic)ayu}^{HA} * cvP_{(black|pelagic)ayu}^{HA})^2 \end{equation}\]

where \(cvP_{(black|pelagic)ayu}^{HA}\) is the coefficient of variation for the hydroacoustic proportions

\[\begin{equation} cvP_{(black|pelagic)ayu}^{HA} ~=~ \frac{\sqrt{varP_{(black|pelagic)ayu}^{HA}}}{P_{(black|pelagic)ayu}^{HA}} \end{equation}\]

and the variance is approximated using the XXXX method as

\[\begin{equation} varP_{(black|pelagic)ayu}^{HA} ~=~ (\frac{1}{n_{pel}})^2 * varN_{black} + (\frac{n_{black}}{n_{pel}^2}) * varN_{pel} \end{equation}\]

where \(varN_{black}\) and \(varN_{black}\) are the variance of the estimated number of black and pelagic rockfish in the hydroacoustic survey, respectively (CITATION).

The average weight of rockfish by species, user, area and year was modeled hierarchically at several levels within regions such that

\[\begin{equation} wt_{(comp)ayu} ~\sim~ Normal(wt_{(comp)au},\sigma_{wt_{(comp)au}}) ~\sim~ Normal(wt_{(comp)a},\sigma_{wt_{(comp)a}}) ~\sim~ Normal(wt_{(comp)region},\sigma_{wt_{(comp)region}}) \end{equation}\]

where region refers to Kodiak, Southcentral and Southeast. Mean weights and variance were calculated as XXX.

Alternative likelihoods for release estimates

To loosen the assumption that logbook release data are an effective census of true releases I explored models that treated logbook release estimates as a lower bound on the estimate of true releases. In a hybrid approach yelloweye and non-pelagic releases are regarded as a reliable census (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates (where censoring implies NA values) such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

This model formulation failed such that there was not enough data to inform pelagic releases and the values did not seem valid. A second approach is being explored that fits the censored data using a lognormal distribution centered around the logbook release value, but also with a lower bound equal to the number of recorded releases such that

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Logbook data is assumed to be a census and as such there is no estimate of uncertainty. As of this writing, several methods are being examined for how to treat \(\sigma_{Ray1}^2\). Models are being run that attempt to allow the model to estimate \(\sigma_{Ray1}^2\) with priors. A simple model applies a uniform prior (0.1,50) to \(\sigma_{Ray1}^2\). A hierarchichal approach based on regions is also being examined whereby \(\sigma_{Ray1}^2\) is lognormally distributed around hyper priors \(\mu_{\sigma_R}\) and \(\sigma_{\sigma_R}\). Initial efforts have applied a uniform prior on \(\mu_{\sigma_R}\) between 1 and 50 and on \(\sigma_{\sigma_R}\) between 0 and 10.

Priors.

Priors range from uninformative to very informative or fixed. Priors for compositional logistic parameters are in Table 2 and proportion harvest logistic parameters are in Table 3. Until I figure out how to make a nice table in Rmarkdown, please refer to the attached spreadsheet and comp and harvp tabs.

Unresolved issues and outstanding questions:

1. Reliability of unguided release estimates: These estimates have the least information feeding them and rely on the bias-corrected SWHS release estimates of all rockfish and the trends in release probability evident in the logbook data. The \(\beta4\) term that estimates the guided/unguided effect was given a very informative prior that tied the release probability of private anglers tightly to that of the charter fleet. The model is then trying to balance the three species complex estimates (pelagic, yelloweye and other) so that they sum to the total unguided releases estimated from the bias corrected SWHS data. For the most part this seems reasonable and appears to work, but there are certain areas where the estimates are “wonky”:

   1. Total rockfish releases more or less align with the total releases estimated with the Howard methods. Presumably, much of the discrepancy results from the substantial bias in release estimates from the SWHS. Interestingly, the logbook data indicates that the SWHS underestimates harvests but overestimates releases by a significant factor (Figure 23 and 24 below).
   2. In general, release estimates of black rockfish are substantially lower than those calculated using the Howard methods. Presumably, much of this derives from the bias correction of the SWHS release estimates.
   3. Yelloweye release estimates also differ considerably from the Howard estimates, but unlike black rockfish are sometimes lower and sometimes higher. Two areas in particular are a little head scratching. Yelloweye releases in the Kodiak Northeast area in particular are significantly lower than for guided anglers with the same pattern evident in Cook Inlet to a lesser extent. Cook Inlet yelloweye numbers are very small, so this is a sample size issue with little consequence. The cause of the Kodiak northeast estimates is not clear to me at this point, but the model estimates the proportion harvested by unguided anglers to be much lower than that of guided anglers, even with the informative prior on \(\beta4\). This must be a product of the bias corrected SWHS release estimates and how the model is partitioning that estimate into the 3 species complexes, but itis a bit a of head scratcher.

2. Proportion guided estimates: There is not much data on this proportion prior to 2011 and it is not modeled with any sort of trend as was done for species composition and harvest proportions. With the exception of Cook Inlet and North Gulf Coast areas, there is little, if any, trend apparent in the data and perhaps this approach is the best available given the data available. However, if there are data sources somewhere that could inform this part of the model they could be incorporated.

3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.

4. Proportion harvest estimates for non-pelagic, non-yelloweye in Kodiak WKMA: I need to adjust the prior on the inflection point, \(\beta3\), so that it is forced to occur after 2006. Right now the model is estimating inflection in two Kodiak areas before that point where there is no data to justify a shift. The current inflection is a result of the hierachichal model.

5. Proportion pelagic in PWS and CSEO: The parameters for these particular proportions are very slow to converge. For the CSEO, the estimates of the \(\beta\) parameters are similar to the other Southeast areas, but the mixing is poor over the length of the chains. In this case I think they will ultimately converge with a very long model run and the shape of the curve in the model output looks acceptable. For the two PWS areas the model seems to struggle with the disparate proportional data from the logbook and the port sampling. There is some wandering in the chains of the \(\beta0\) and \(\beta1\) terms and spikiness in the \(\beta2\) terms. I’ve been working on constraining the hyperpriors for PWS \(beta2\). Similar to CSEO, it may just entail a very long model run to reach convergence, but the shape of the curves looks reasonable.

Next steps:

Once the model is finalized, harvest and release numbers need to be converted into biomass removals. This is a two step process where release mortality estimates are applied to the release estimates to estimate the number of released rockfish that do not survive. This is based on studies and will reflect the values that the department has been using with the Howard methods. Region 2 (both Southcentral and Kodiak) have release-at-depth estimates from a number of years that they apply across all years and then calculate mortality rates based on those estiates. Southease does not have release-at-depth data and simply applies an assumed rate based on research.

Once release mortality is calculated average weight data is applied to convert numbers to biomass. The plan is to incorporate all of this into the model to propogate uncertainty into the posteriors. However, the model already takes a long time to run and I may explore a simpler approach using the posteriors from the numbers model to speed up processing.

Results

• Model: LB_fit_3pH

• Model Run: rf_harvest_est_kha_rm_wt_thru2023_480000_7kn_2025-05-23 (Naming convention: modelname_thruYEAR_iters_rundate)

• Proportion of parmaters converged (Rhat <= 1.1): 0.9921

• See end of document for summary of unconverged parameters.

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

Figure 3.- Total rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

And black rockfish releases…

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 8.- DSR rockfish (including yelloweye) harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 9.- DSR rockfish releases (including yelloweye) 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 11.- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 12.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Total Biomass Removal Estimates

Figure 13.- Black rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 14.- Yellow rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 15.- Pelagic rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 16.- Non-yelloweye, demersal shelf rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 17.- Slope rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Model fit

Logbook residuals

Figure 18.- Residuals from logbook harvests.

SWHS residuals

Figure 19.- Residuals from SWHS harvests.

Figure 20.- Residual of SWHS releases.

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

Figure 21.- Mean percent of harvest by charter anglers.

When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although the model smooths out the changes and we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

Figure 22.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.

Figure 23.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 24.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 25.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

## NULL

## NULL

SWHS bias

Figure 23 shows the mean estimate for SWHS bias in harvests and releases. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias. Bias in release estimates is substantial and whereas the SWHS appears to underestimate harvests, it appears to greatly overestimates releases by a factor of 2 or more in most areas as derived from logbook reported releases.

Figure 28.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

Our estimates of SWHS harvest bias track observations fairly well when he have guided harvest estimates. The estimates of release bias in the SWHS data track observed patterns to an extent, but appear to smooth these more volatile disagreements with the logbook data. Adam postulated in his initial start on this that some of this could be the result of the estimates of the proportion guided. This value was not modelled with a trend and thus applies a constant estimate when hindcasting. Data on these relationships could greatly improve this model.

Figure 29.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 25 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

Figure 30.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment. For the most part, P(black|pelagic) is relatively constant across areas, with the exception of Cook Inlet and NSEI in Southeast AK. It may be worth discussing whether the shifts in those areas is a result of improved or changing species identification rather than actual shift in the species composition of the catch.

Figure 31.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023. Kodiak panels include data from a hydroacoustic survey and the proportion of pelagic rockfish that are black in those areas (red) and the adjusted proportions based on obseved harvests for charter (blue) and private (cyan) users.

P(yelloweye|non-pelagic / yelloweye|DSR)

Figure 32.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

Figure 33.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

Figure 34.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(slope|non-pelagic & non-yellowye) For release estimates

Figure 35.- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.

Weight Fits

Figure 36.- Mean weights of black rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 37.- Mean weights of yelloweye rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 38.- Mean weights of non-black, pelagic rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 39.- Mean weights of non-yelloweye, demersal shelf rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 40.- Mean weights of slope rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

### Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.

parameter n badRhat_avg beta1_pelagic 5 1.497782 beta0_pelagic 3 1.411919 beta3_pH 3 1.297780 beta3_pelagic 1 1.284141 beta0_black 1 1.279525 beta2_yellow 4 1.276119 beta1_pH 8 1.260555 beta0_pH 6 1.258919

parameter n badRhat_avg beta2_pH 13 1.233590 beta2_pelagic 6 1.228693 beta3_yellow 1 1.179085 beta4_pelagic 1 1.165358 beta1_yellow 2 1.145926 beta0_yellow 3 1.134571 tau_beta0_pH 1 1.113793

Table 2. Summary of unconverged parameters by area

	afognak	CI	CSEO	EWYKT	NG	northeast	NSEI	NSEO	PWSI	PWSO	SSEI	SSEO	WKMA
beta0_black	1	0	0	0	0	0	0	0	0	0	0	0	0
beta0_pelagic	0	0	1	0	0	0	0	0	0	1	0	1	0
beta0_pH	0	1	1	0	0	1	1	0	0	1	0	1	0
beta0_yellow	0	0	1	0	0	0	0	0	0	1	1	0	0
beta1_pelagic	0	0	1	0	0	0	0	1	1	1	0	1	0
beta1_pH	0	1	1	0	0	1	1	0	1	1	0	1	0
beta1_yellow	0	0	1	0	0	0	0	0	0	0	1	0	0
beta2_pelagic	0	0	1	1	0	0	1	0	1	0	1	1	0
beta2_pH	0	1	1	1	1	1	1	1	1	1	1	1	1
beta2_yellow	0	1	0	0	1	0	0	0	1	1	0	0	0
beta3_pelagic	0	0	1	0	0	0	0	0	0	0	0	0	0
beta3_pH	0	0	0	0	0	1	1	0	0	1	0	0	0
beta3_yellow	0	0	1	0	0	0	0	0	0	0	0	0	0
beta4_pelagic	0	0	0	0	0	0	0	0	0	0	0	1	0
tau_beta0_pH	0	1	0	0	0	0	0	0	0	0	0	0	0

Parameter estimates:

Summary Table of Parameter Estimates

Parameter	mean	sd	Lower_CI	Median	Upper_CI
mu_bc_H[1]	-0.125	0.074	-0.261	-0.128	0.030
mu_bc_H[2]	-0.095	0.047	-0.174	-0.098	0.007
mu_bc_H[3]	-0.432	0.073	-0.574	-0.432	-0.285
mu_bc_H[4]	-0.997	0.191	-1.377	-0.992	-0.635
mu_bc_H[5]	0.903	0.950	-0.198	0.715	3.237
mu_bc_H[6]	-2.132	0.334	-2.803	-2.137	-1.471
mu_bc_H[7]	-0.456	0.107	-0.674	-0.454	-0.254
mu_bc_H[8]	0.251	0.365	-0.330	0.206	1.083
mu_bc_H[9]	-0.297	0.136	-0.564	-0.297	-0.032
mu_bc_H[10]	-0.104	0.072	-0.236	-0.107	0.045
mu_bc_H[11]	-0.126	0.039	-0.201	-0.126	-0.050
mu_bc_H[12]	-0.250	0.108	-0.487	-0.247	-0.044
mu_bc_H[13]	-0.130	0.075	-0.279	-0.131	0.022
mu_bc_H[14]	-0.305	0.098	-0.510	-0.303	-0.120
mu_bc_H[15]	-0.342	0.049	-0.438	-0.343	-0.243
mu_bc_H[16]	-0.291	0.383	-0.949	-0.323	0.510
mu_bc_R[1]	1.301	0.148	1.022	1.295	1.602
mu_bc_R[2]	1.457	0.093	1.268	1.457	1.636
mu_bc_R[3]	1.392	0.140	1.108	1.395	1.662
mu_bc_R[4]	0.921	0.208	0.492	0.930	1.302
mu_bc_R[5]	1.185	0.470	0.250	1.197	2.078
mu_bc_R[6]	-1.587	0.421	-2.413	-1.581	-0.769
mu_bc_R[7]	0.457	0.205	0.035	0.464	0.839
mu_bc_R[8]	0.564	0.195	0.170	0.567	0.943
mu_bc_R[9]	0.355	0.199	-0.083	0.367	0.712
mu_bc_R[10]	1.307	0.136	1.027	1.309	1.562
mu_bc_R[11]	1.046	0.095	0.858	1.046	1.238
mu_bc_R[12]	0.813	0.204	0.403	0.818	1.206
mu_bc_R[13]	1.027	0.104	0.818	1.029	1.228
mu_bc_R[14]	0.902	0.139	0.620	0.905	1.171
mu_bc_R[15]	0.781	0.110	0.558	0.781	0.991
mu_bc_R[16]	1.096	0.128	0.839	1.093	1.351
tau_pH[1]	4.904	0.781	2.647	5.042	5.997
tau_pH[2]	2.026	0.223	1.616	2.014	2.493
tau_pH[3]	2.099	0.240	1.649	2.097	2.573
beta0_pH[1,1]	0.570	0.195	0.216	0.568	0.948
beta0_pH[2,1]	1.399	0.189	1.011	1.401	1.764
beta0_pH[3,1]	1.452	0.198	1.040	1.460	1.812
beta0_pH[4,1]	1.642	0.326	1.129	1.613	2.806
beta0_pH[5,1]	-0.820	0.302	-1.450	-0.809	-0.273
beta0_pH[6,1]	-0.716	0.502	-2.067	-0.624	-0.027
beta0_pH[7,1]	-0.309	0.470	-1.249	-0.334	0.709
beta0_pH[8,1]	-0.654	0.284	-1.395	-0.622	-0.200
beta0_pH[9,1]	-0.586	0.295	-1.238	-0.575	-0.040
beta0_pH[10,1]	0.383	0.429	-0.134	0.289	1.642
beta0_pH[11,1]	-0.126	0.250	-0.517	-0.139	0.311
beta0_pH[12,1]	0.461	0.202	0.083	0.463	0.848
beta0_pH[13,1]	0.014	0.167	-0.291	0.008	0.362
beta0_pH[14,1]	-0.285	0.196	-0.630	-0.297	0.169
beta0_pH[15,1]	-0.031	0.187	-0.399	-0.028	0.334
beta0_pH[16,1]	-0.416	0.419	-1.592	-0.341	0.200
beta0_pH[1,2]	2.842	0.161	2.514	2.849	3.162
beta0_pH[2,2]	2.894	0.136	2.625	2.894	3.164
beta0_pH[3,2]	3.133	0.161	2.846	3.130	3.456
beta0_pH[4,2]	2.944	0.132	2.675	2.944	3.201
beta0_pH[5,2]	4.855	1.458	2.997	4.555	8.503
beta0_pH[6,2]	3.111	0.206	2.713	3.113	3.508
beta0_pH[7,2]	1.840	0.198	1.443	1.846	2.218
beta0_pH[8,2]	2.870	0.174	2.533	2.867	3.213
beta0_pH[9,2]	3.426	0.222	2.998	3.421	3.864
beta0_pH[10,2]	3.758	0.198	3.382	3.756	4.157
beta0_pH[11,2]	-4.845	0.288	-5.419	-4.844	-4.278
beta0_pH[12,2]	-4.761	0.378	-5.499	-4.757	-4.044
beta0_pH[13,2]	-4.576	0.396	-5.343	-4.586	-3.787
beta0_pH[14,2]	-5.569	0.459	-6.602	-5.537	-4.767
beta0_pH[15,2]	-4.295	0.336	-4.916	-4.299	-3.620
beta0_pH[16,2]	-4.846	0.379	-5.622	-4.838	-4.147
beta0_pH[1,3]	0.006	0.754	-1.744	0.108	1.207
beta0_pH[2,3]	2.194	0.161	1.879	2.199	2.512
beta0_pH[3,3]	2.525	0.152	2.228	2.523	2.827
beta0_pH[4,3]	2.964	0.165	2.645	2.965	3.293
beta0_pH[5,3]	2.118	1.365	0.404	1.835	5.671
beta0_pH[6,3]	0.986	0.497	-0.203	1.043	1.835
beta0_pH[7,3]	0.621	0.169	0.295	0.623	0.957
beta0_pH[8,3]	0.306	0.197	-0.076	0.309	0.685
beta0_pH[9,3]	-0.644	0.403	-1.700	-0.600	0.008
beta0_pH[10,3]	0.443	0.409	-0.545	0.504	1.062
beta0_pH[11,3]	0.044	0.512	-0.926	0.058	1.036
beta0_pH[12,3]	-0.859	0.408	-1.665	-0.854	-0.144
beta0_pH[13,3]	-0.040	0.460	-0.982	-0.040	0.879
beta0_pH[14,3]	-0.215	0.315	-0.797	-0.229	0.405
beta0_pH[15,3]	-0.695	0.334	-1.352	-0.712	-0.030
beta0_pH[16,3]	-0.318	0.337	-0.945	-0.328	0.336
beta1_pH[1,1]	3.055	0.339	2.403	3.045	3.759
beta1_pH[2,1]	2.112	0.302	1.571	2.102	2.722
beta1_pH[3,1]	1.925	0.316	1.333	1.914	2.619
beta1_pH[4,1]	2.322	0.484	1.538	2.298	3.294
beta1_pH[5,1]	2.260	0.359	1.645	2.228	3.050
beta1_pH[6,1]	3.907	1.269	2.191	3.677	7.217
beta1_pH[7,1]	2.230	0.918	0.288	2.283	3.965
beta1_pH[8,1]	4.073	1.118	2.536	3.818	6.932
beta1_pH[9,1]	2.228	0.380	1.484	2.208	3.044
beta1_pH[10,1]	2.189	0.623	0.071	2.316	2.894
beta1_pH[11,1]	3.302	0.278	2.760	3.315	3.767
beta1_pH[12,1]	2.580	0.233	2.110	2.581	3.014
beta1_pH[13,1]	2.960	0.244	2.445	2.965	3.415
beta1_pH[14,1]	3.385	0.249	2.847	3.390	3.848
beta1_pH[15,1]	2.543	0.229	2.114	2.542	2.989
beta1_pH[16,1]	3.982	0.738	2.986	3.837	6.044
beta1_pH[1,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[2,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[3,2]	0.007	0.091	0.000	0.000	0.001
beta1_pH[4,2]	0.000	0.000	0.000	0.000	0.001
beta1_pH[5,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[6,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[7,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[8,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[9,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[10,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[11,2]	6.688	0.328	6.071	6.681	7.346
beta1_pH[12,2]	6.418	0.440	5.598	6.414	7.342
beta1_pH[13,2]	6.967	0.431	6.159	6.959	7.826
beta1_pH[14,2]	7.217	0.485	6.364	7.186	8.306
beta1_pH[15,2]	6.773	0.370	6.030	6.782	7.502
beta1_pH[16,2]	7.448	0.417	6.638	7.448	8.315
beta1_pH[1,3]	4.158	1.657	1.781	3.766	7.781
beta1_pH[2,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[3,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[4,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[5,3]	3.432	3.054	0.828	2.796	11.041
beta1_pH[6,3]	2.948	2.271	0.452	2.621	8.396
beta1_pH[7,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[8,3]	2.755	0.348	2.086	2.752	3.442
beta1_pH[9,3]	2.767	0.476	2.009	2.721	3.943
beta1_pH[10,3]	2.934	0.479	2.194	2.878	4.144
beta1_pH[11,3]	2.488	0.611	1.101	2.493	3.692
beta1_pH[12,3]	4.110	0.535	3.197	4.124	5.095
beta1_pH[13,3]	1.615	0.485	0.568	1.615	2.598
beta1_pH[14,3]	2.437	0.419	1.659	2.464	3.190
beta1_pH[15,3]	1.975	0.368	1.248	1.992	2.677
beta1_pH[16,3]	1.712	0.380	0.976	1.718	2.427
beta2_pH[1,1]	0.545	0.680	0.286	0.469	0.887
beta2_pH[2,1]	0.702	0.827	0.247	0.538	2.228
beta2_pH[3,1]	0.827	1.124	0.231	0.577	3.359
beta2_pH[4,1]	0.568	1.168	-1.169	0.456	1.509
beta2_pH[5,1]	1.469	1.021	0.241	1.321	3.842
beta2_pH[6,1]	0.179	0.120	0.074	0.172	0.352
beta2_pH[7,1]	0.029	0.154	0.000	0.000	0.241
beta2_pH[8,1]	0.245	0.106	0.115	0.227	0.462
beta2_pH[9,1]	0.488	0.350	0.200	0.418	1.185
beta2_pH[10,1]	0.466	0.558	-0.877	0.517	1.233
beta2_pH[11,1]	0.845	0.920	0.464	0.734	1.484
beta2_pH[12,1]	1.374	0.995	0.699	1.197	2.676
beta2_pH[13,1]	0.813	1.004	0.411	0.704	1.347
beta2_pH[14,1]	0.990	1.342	0.519	0.804	1.599
beta2_pH[15,1]	0.896	1.034	0.416	0.749	1.767
beta2_pH[16,1]	0.542	1.115	0.155	0.372	1.135
beta2_pH[1,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[2,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[3,2]	-2.045	1.865	-6.846	-1.531	-0.027
beta2_pH[4,2]	-1.979	1.866	-6.950	-1.445	-0.031
beta2_pH[5,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[6,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[7,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[8,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[9,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[10,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[11,2]	-9.299	4.351	-20.567	-8.288	-3.925
beta2_pH[12,2]	-7.897	5.056	-20.379	-7.027	-1.046
beta2_pH[13,2]	-7.753	5.022	-20.374	-6.728	-1.684
beta2_pH[14,2]	-8.421	4.707	-20.416	-7.358	-2.473
beta2_pH[15,2]	-9.189	4.460	-20.936	-8.207	-3.835
beta2_pH[16,2]	-9.396	4.331	-20.281	-8.354	-4.056
beta2_pH[1,3]	0.325	0.547	0.101	0.222	1.119
beta2_pH[2,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[3,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[4,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[5,3]	8.827	6.403	-0.315	7.846	23.704
beta2_pH[6,3]	8.946	6.290	0.134	7.992	23.319
beta2_pH[7,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[8,3]	9.875	5.768	1.653	8.795	23.433
beta2_pH[9,3]	8.837	6.342	0.476	7.605	23.471
beta2_pH[10,3]	8.331	6.490	0.483	7.279	23.871
beta2_pH[11,3]	-3.012	3.101	-12.679	-1.925	-0.531
beta2_pH[12,3]	-2.873	2.863	-11.527	-1.943	-0.916
beta2_pH[13,3]	-3.011	3.466	-12.527	-2.162	2.275
beta2_pH[14,3]	-3.403	3.050	-12.223	-2.363	-0.880
beta2_pH[15,3]	-3.622	3.090	-12.647	-2.566	-0.926
beta2_pH[16,3]	-3.605	3.125	-12.534	-2.521	-0.852
beta3_pH[1,1]	35.999	0.926	34.333	35.963	37.839
beta3_pH[2,1]	33.662	1.290	31.490	33.538	36.690
beta3_pH[3,1]	33.581	1.061	31.538	33.555	35.814
beta3_pH[4,1]	33.438	2.789	21.047	33.704	36.563
beta3_pH[5,1]	27.782	1.204	26.482	27.506	31.246
beta3_pH[6,1]	38.475	3.484	32.514	38.311	45.082
beta3_pH[7,1]	30.744	7.911	18.635	30.486	44.968
beta3_pH[8,1]	40.131	2.496	35.531	39.904	45.185
beta3_pH[9,1]	30.676	1.433	28.054	30.611	33.665
beta3_pH[10,1]	31.972	3.728	18.800	32.678	35.070
beta3_pH[11,1]	30.206	0.541	29.278	30.185	31.199
beta3_pH[12,1]	30.124	0.425	29.288	30.122	30.934
beta3_pH[13,1]	33.170	0.607	32.050	33.152	34.439
beta3_pH[14,1]	32.063	0.536	31.135	32.032	33.194
beta3_pH[15,1]	31.207	0.710	29.923	31.175	32.639
beta3_pH[16,1]	31.967	1.166	30.259	31.819	34.550
beta3_pH[1,2]	29.867	8.046	18.466	28.638	44.854
beta3_pH[2,2]	30.023	7.949	18.474	29.048	44.757
beta3_pH[3,2]	29.952	8.082	18.380	28.811	44.884
beta3_pH[4,2]	29.745	7.914	18.424	28.734	44.966
beta3_pH[5,2]	30.226	8.014	18.502	29.271	45.020
beta3_pH[6,2]	29.870	7.918	18.444	28.814	44.793
beta3_pH[7,2]	29.910	7.948	18.466	29.153	44.791
beta3_pH[8,2]	29.913	7.903	18.459	28.995	44.807
beta3_pH[9,2]	29.986	8.081	18.456	29.098	44.923
beta3_pH[10,2]	29.813	7.992	18.401	28.831	44.916
beta3_pH[11,2]	43.401	0.180	43.117	43.379	43.771
beta3_pH[12,2]	43.195	0.200	42.922	43.142	43.738
beta3_pH[13,2]	43.863	0.147	43.469	43.902	44.041
beta3_pH[14,2]	43.293	0.204	43.043	43.236	43.811
beta3_pH[15,2]	43.405	0.192	43.102	43.385	43.810
beta3_pH[16,2]	43.490	0.187	43.159	43.486	43.841
beta3_pH[1,3]	38.472	3.194	32.061	38.463	44.936
beta3_pH[2,3]	30.475	7.952	18.512	29.923	44.868
beta3_pH[3,3]	30.240	8.156	18.428	29.445	45.047
beta3_pH[4,3]	30.273	8.056	18.514	29.603	45.040
beta3_pH[5,3]	36.744	3.864	31.237	36.126	45.053
beta3_pH[6,3]	40.301	3.586	31.752	40.764	45.603
beta3_pH[7,3]	38.088	4.327	31.311	37.849	45.538
beta3_pH[8,3]	41.485	0.262	41.052	41.482	41.940
beta3_pH[9,3]	33.443	0.608	31.545	33.545	34.325
beta3_pH[10,3]	35.787	0.823	33.377	36.001	36.833
beta3_pH[11,3]	41.529	1.005	39.564	41.552	43.509
beta3_pH[12,3]	41.719	0.420	40.955	41.744	42.525
beta3_pH[13,3]	41.995	3.048	30.651	42.707	45.207
beta3_pH[14,3]	41.046	0.741	39.711	41.094	42.231
beta3_pH[15,3]	42.729	0.821	41.164	42.845	43.862
beta3_pH[16,3]	42.808	0.933	40.820	42.983	44.128
beta0_pelagic[1]	2.221	0.132	1.966	2.221	2.480
beta0_pelagic[2]	1.505	0.120	1.272	1.506	1.745
beta0_pelagic[3]	0.012	0.390	-0.954	0.074	0.633
beta0_pelagic[4]	-0.057	0.570	-1.368	-0.010	0.836
beta0_pelagic[5]	1.190	0.253	0.686	1.190	1.694
beta0_pelagic[6]	1.453	0.274	0.872	1.475	1.947
beta0_pelagic[7]	1.583	0.210	1.181	1.576	2.028
beta0_pelagic[8]	1.762	0.217	1.348	1.753	2.208
beta0_pelagic[9]	2.486	0.317	1.860	2.494	3.065
beta0_pelagic[10]	2.529	0.208	2.089	2.535	2.918
beta0_pelagic[11]	-0.462	0.497	-1.527	-0.433	0.431
beta0_pelagic[12]	1.683	0.145	1.399	1.686	1.971
beta0_pelagic[13]	0.224	0.279	-0.637	0.269	0.634
beta0_pelagic[14]	-0.156	0.299	-0.916	-0.126	0.323
beta0_pelagic[15]	-0.267	0.141	-0.535	-0.268	0.021
beta0_pelagic[16]	0.248	0.257	-0.335	0.289	0.635
beta1_pelagic[1]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[2]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[3]	1.319	0.658	0.380	1.181	2.966
beta1_pelagic[4]	1.343	0.629	0.263	1.269	2.691
beta1_pelagic[5]	-0.071	0.319	-0.701	-0.069	0.538
beta1_pelagic[6]	-0.082	0.461	-0.866	-0.127	0.752
beta1_pelagic[7]	-0.009	0.291	-0.554	-0.013	0.574
beta1_pelagic[8]	-0.012	0.287	-0.585	-0.018	0.556
beta1_pelagic[9]	0.201	0.490	-0.787	0.318	0.960
beta1_pelagic[10]	0.057	0.273	-0.480	0.056	0.595
beta1_pelagic[11]	4.937	1.225	2.822	4.958	7.407
beta1_pelagic[12]	2.824	0.360	2.189	2.802	3.630
beta1_pelagic[13]	3.281	0.817	1.871	3.291	4.871
beta1_pelagic[14]	4.816	0.957	3.201	4.723	6.843
beta1_pelagic[15]	2.954	0.280	2.338	2.958	3.459
beta1_pelagic[16]	3.814	0.970	2.716	3.470	6.444
beta2_pelagic[1]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[2]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[3]	1.057	2.733	0.054	0.249	9.528
beta2_pelagic[4]	1.757	3.780	0.068	0.479	15.552
beta2_pelagic[5]	-0.042	0.679	-1.537	-0.027	1.375
beta2_pelagic[6]	-0.082	0.701	-1.476	-0.122	1.394
beta2_pelagic[7]	0.014	0.639	-1.342	0.003	1.356
beta2_pelagic[8]	0.189	0.625	-0.910	0.090	1.594
beta2_pelagic[9]	0.173	0.699	-1.404	0.258	1.493
beta2_pelagic[10]	0.056	0.632	-1.237	0.034	1.494
beta2_pelagic[11]	0.205	0.185	0.094	0.157	0.660
beta2_pelagic[12]	5.136	4.604	0.740	3.719	18.113
beta2_pelagic[13]	0.610	1.046	0.133	0.368	2.688
beta2_pelagic[14]	0.282	0.107	0.142	0.263	0.572
beta2_pelagic[15]	5.427	4.587	1.090	4.088	18.558
beta2_pelagic[16]	3.614	4.906	0.208	0.968	17.302
beta3_pelagic[1]	29.892	7.946	18.516	28.993	45.073
beta3_pelagic[2]	29.850	7.958	18.476	28.521	44.856
beta3_pelagic[3]	31.064	5.559	20.996	30.358	43.377
beta3_pelagic[4]	25.284	4.220	19.401	24.756	37.721
beta3_pelagic[5]	29.955	8.190	18.463	28.564	45.233
beta3_pelagic[6]	31.706	6.716	19.042	31.643	44.417
beta3_pelagic[7]	29.820	7.919	18.509	28.741	44.931
beta3_pelagic[8]	29.320	7.964	18.459	27.755	44.912
beta3_pelagic[9]	31.010	6.040	19.438	31.093	43.594
beta3_pelagic[10]	29.704	8.272	18.410	28.209	45.156
beta3_pelagic[11]	42.218	2.843	33.735	42.712	45.840
beta3_pelagic[12]	43.479	0.318	42.961	43.455	44.153
beta3_pelagic[13]	43.130	1.444	40.034	43.133	45.761
beta3_pelagic[14]	42.958	1.585	39.640	42.940	45.770
beta3_pelagic[15]	43.139	0.270	42.537	43.149	43.665
beta3_pelagic[16]	43.091	0.959	40.531	43.196	45.100
mu_beta0_pelagic[1]	0.857	0.969	-1.255	0.889	2.773
mu_beta0_pelagic[2]	1.805	0.399	0.972	1.815	2.589
mu_beta0_pelagic[3]	0.203	0.501	-0.823	0.220	1.138
tau_beta0_pelagic[1]	0.611	0.649	0.054	0.410	2.377
tau_beta0_pelagic[2]	2.621	2.553	0.249	1.930	8.923
tau_beta0_pelagic[3]	1.285	1.015	0.155	1.012	3.998
beta0_yellow[1]	-0.536	0.188	-0.959	-0.522	-0.218
beta0_yellow[2]	0.493	0.153	0.179	0.497	0.787
beta0_yellow[3]	-0.327	0.183	-0.712	-0.317	0.002
beta0_yellow[4]	0.782	0.353	-0.231	0.858	1.209
beta0_yellow[5]	-0.281	0.356	-0.981	-0.286	0.436
beta0_yellow[6]	1.118	0.163	0.808	1.115	1.441
beta0_yellow[7]	0.984	0.160	0.680	0.979	1.315
beta0_yellow[8]	1.010	0.155	0.701	1.012	1.315
beta0_yellow[9]	0.658	0.159	0.348	0.658	0.978
beta0_yellow[10]	0.581	0.142	0.304	0.582	0.858
beta0_yellow[11]	-1.937	0.447	-2.799	-1.961	-0.958
beta0_yellow[12]	-3.690	0.412	-4.520	-3.681	-2.912
beta0_yellow[13]	-3.729	0.538	-4.969	-3.678	-2.819
beta0_yellow[14]	-2.104	0.501	-3.024	-2.127	-1.074
beta0_yellow[15]	-2.833	0.456	-3.870	-2.774	-2.062
beta0_yellow[16]	-2.347	0.452	-3.204	-2.357	-1.428
beta1_yellow[1]	0.803	1.063	0.008	0.641	2.601
beta1_yellow[2]	1.075	0.314	0.609	1.045	1.765
beta1_yellow[3]	0.725	0.266	0.243	0.703	1.315
beta1_yellow[4]	1.485	0.850	0.661	1.224	4.029
beta1_yellow[5]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[6]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[7]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[8]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[9]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[10]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[11]	2.094	0.465	1.145	2.128	2.905
beta1_yellow[12]	2.481	0.424	1.669	2.464	3.359
beta1_yellow[13]	2.845	0.536	1.952	2.783	4.131
beta1_yellow[14]	2.178	0.515	1.127	2.191	3.107
beta1_yellow[15]	2.073	0.456	1.280	2.030	3.127
beta1_yellow[16]	2.107	0.461	1.118	2.133	2.955
beta2_yellow[1]	-2.883	2.394	-8.701	-2.337	-0.029
beta2_yellow[2]	-2.740	1.985	-6.285	-2.305	-0.205
beta2_yellow[3]	-2.441	2.032	-7.648	-1.922	-0.142
beta2_yellow[4]	-2.003	2.034	-6.486	-1.122	-0.085
beta2_yellow[5]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[6]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[7]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[8]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[9]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[10]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[11]	-4.816	2.712	-11.296	-4.322	-1.121
beta2_yellow[12]	-5.205	2.850	-12.500	-4.583	-1.416
beta2_yellow[13]	-4.860	2.601	-11.555	-4.268	-1.463
beta2_yellow[14]	-5.066	3.027	-12.576	-4.457	-0.746
beta2_yellow[15]	-4.586	2.872	-11.935	-3.872	-1.048
beta2_yellow[16]	-5.171	2.808	-12.223	-4.596	-1.376
beta3_yellow[1]	25.631	6.980	18.260	22.624	43.665
beta3_yellow[2]	29.130	1.836	25.262	28.947	32.886
beta3_yellow[3]	32.967	2.921	25.973	32.967	39.054
beta3_yellow[4]	29.228	4.006	20.785	28.250	36.938
beta3_yellow[5]	29.975	8.021	18.416	29.115	44.949
beta3_yellow[6]	29.732	7.941	18.403	28.739	44.773
beta3_yellow[7]	30.165	7.909	18.474	29.414	44.963
beta3_yellow[8]	29.903	7.925	18.484	28.979	44.862
beta3_yellow[9]	30.032	7.917	18.481	29.129	44.834
beta3_yellow[10]	30.613	8.104	18.531	30.027	45.143
beta3_yellow[11]	45.220	0.850	43.720	45.369	45.970
beta3_yellow[12]	43.311	0.382	42.554	43.285	44.074
beta3_yellow[13]	44.864	0.408	43.967	44.945	45.552
beta3_yellow[14]	44.249	0.964	43.053	44.242	45.863
beta3_yellow[15]	45.132	0.530	44.139	45.103	45.970
beta3_yellow[16]	44.555	0.648	43.401	44.530	45.824
mu_beta0_yellow[1]	0.086	0.554	-1.059	0.076	1.248
mu_beta0_yellow[2]	0.648	0.327	-0.050	0.672	1.250
mu_beta0_yellow[3]	-2.412	0.638	-3.409	-2.513	-0.891
tau_beta0_yellow[1]	1.896	2.502	0.099	1.212	7.863
tau_beta0_yellow[2]	3.583	4.345	0.327	2.396	13.709
tau_beta0_yellow[3]	1.366	2.048	0.098	0.877	5.236
beta0_black[1]	-0.075	0.156	-0.365	-0.076	0.233
beta0_black[2]	1.915	0.131	1.666	1.914	2.176
beta0_black[3]	1.317	0.136	1.047	1.319	1.579
beta0_black[4]	2.428	0.136	2.163	2.425	2.692
beta0_black[5]	4.598	2.078	1.860	4.127	10.090
beta0_black[6]	4.603	1.917	2.206	4.130	9.699
beta0_black[7]	3.772	1.874	1.553	3.294	8.830
beta0_black[8]	1.022	0.244	0.560	1.021	1.519
beta0_black[9]	2.595	0.234	2.152	2.590	3.059
beta0_black[10]	1.458	0.134	1.190	1.454	1.723
beta0_black[11]	3.483	0.156	3.173	3.481	3.788
beta0_black[12]	4.869	0.171	4.520	4.867	5.198
beta0_black[13]	-0.113	0.247	-0.619	-0.108	0.348
beta0_black[14]	2.853	0.156	2.539	2.854	3.163
beta0_black[15]	1.296	0.155	0.978	1.298	1.594
beta0_black[16]	4.278	0.159	3.962	4.279	4.583
beta2_black[1]	7.693	10.039	0.571	3.384	40.092
beta2_black[2]	0.000	0.000	0.000	0.000	0.000
beta2_black[3]	0.000	0.000	0.000	0.000	0.000
beta2_black[4]	0.000	0.000	0.000	0.000	0.000
beta2_black[5]	0.000	0.000	0.000	0.000	0.000
beta2_black[6]	0.000	0.000	0.000	0.000	0.000
beta2_black[7]	0.000	0.000	0.000	0.000	0.000
beta2_black[8]	0.000	0.000	0.000	0.000	0.000
beta2_black[9]	0.000	0.000	0.000	0.000	0.000
beta2_black[10]	0.000	0.000	0.000	0.000	0.000
beta2_black[11]	0.000	0.000	0.000	0.000	0.000
beta2_black[12]	0.000	0.000	0.000	0.000	0.000
beta2_black[13]	-1.796	1.508	-5.985	-1.312	-0.295
beta2_black[14]	0.000	0.000	0.000	0.000	0.000
beta2_black[15]	0.000	0.000	0.000	0.000	0.000
beta2_black[16]	0.000	0.000	0.000	0.000	0.000
beta3_black[1]	41.761	1.132	39.776	41.910	43.224
beta3_black[2]	25.000	0.000	25.000	25.000	25.000
beta3_black[3]	25.000	0.000	25.000	25.000	25.000
beta3_black[4]	25.000	0.000	25.000	25.000	25.000
beta3_black[5]	25.000	0.000	25.000	25.000	25.000
beta3_black[6]	25.000	0.000	25.000	25.000	25.000
beta3_black[7]	25.000	0.000	25.000	25.000	25.000
beta3_black[8]	25.000	0.000	25.000	25.000	25.000
beta3_black[9]	25.000	0.000	25.000	25.000	25.000
beta3_black[10]	25.000	0.000	25.000	25.000	25.000
beta3_black[11]	25.000	0.000	25.000	25.000	25.000
beta3_black[12]	25.000	0.000	25.000	25.000	25.000
beta3_black[13]	39.115	0.986	36.788	39.251	40.551
beta3_black[14]	25.000	0.000	25.000	25.000	25.000
beta3_black[15]	25.000	0.000	25.000	25.000	25.000
beta3_black[16]	25.000	0.000	25.000	25.000	25.000
beta4_black[1]	-0.257	0.195	-0.626	-0.257	0.126
beta4_black[2]	0.237	0.190	-0.129	0.236	0.614
beta4_black[3]	-0.935	0.199	-1.315	-0.932	-0.540
beta4_black[4]	0.425	0.221	-0.006	0.426	0.847
beta4_black[5]	0.558	1.270	-1.328	0.352	3.764
beta4_black[6]	0.533	1.297	-1.360	0.301	3.735
beta4_black[7]	0.434	1.238	-1.475	0.244	3.222
beta4_black[8]	-0.306	0.336	-0.995	-0.303	0.321
beta4_black[9]	0.867	0.802	-0.270	0.710	2.877
beta4_black[10]	0.049	0.186	-0.315	0.049	0.407
beta4_black[11]	-0.696	0.217	-1.125	-0.696	-0.270
beta4_black[12]	0.171	0.320	-0.438	0.163	0.828
beta4_black[13]	-1.187	0.226	-1.634	-1.183	-0.749
beta4_black[14]	-0.178	0.229	-0.624	-0.184	0.279
beta4_black[15]	-0.892	0.215	-1.315	-0.886	-0.477
beta4_black[16]	-0.593	0.224	-1.034	-0.589	-0.163
mu_beta0_black[1]	1.255	0.881	-0.760	1.304	2.935
mu_beta0_black[2]	2.689	1.048	0.735	2.599	4.963
mu_beta0_black[3]	2.494	1.001	0.297	2.547	4.326
tau_beta0_black[1]	0.636	0.581	0.057	0.458	2.182
tau_beta0_black[2]	0.472	0.756	0.047	0.244	2.347
tau_beta0_black[3]	0.235	0.154	0.051	0.197	0.626
beta0_dsr[11]	-2.906	0.273	-3.447	-2.905	-2.371
beta0_dsr[12]	4.559	0.292	3.991	4.556	5.126
beta0_dsr[13]	-1.366	0.344	-1.985	-1.352	-0.789
beta0_dsr[14]	-3.688	0.524	-4.730	-3.674	-2.696
beta0_dsr[15]	-1.957	0.284	-2.506	-1.954	-1.400
beta0_dsr[16]	-3.014	0.362	-3.731	-3.009	-2.304
beta1_dsr[11]	4.834	0.292	4.249	4.838	5.414
beta1_dsr[12]	8.367	36.554	2.278	5.126	23.079
beta1_dsr[13]	2.873	0.395	2.277	2.851	3.546
beta1_dsr[14]	6.352	0.552	5.313	6.328	7.493
beta1_dsr[15]	3.353	0.288	2.785	3.355	3.908
beta1_dsr[16]	5.825	0.380	5.082	5.824	6.577
beta2_dsr[11]	-8.382	2.348	-13.729	-8.092	-4.648
beta2_dsr[12]	-7.178	2.753	-13.140	-6.980	-2.314
beta2_dsr[13]	-6.682	2.865	-12.850	-6.427	-1.604
beta2_dsr[14]	-6.260	2.744	-12.116	-6.022	-1.794
beta2_dsr[15]	-7.964	2.535	-13.896	-7.688	-4.033
beta2_dsr[16]	-8.079	2.471	-13.623	-7.755	-4.257
beta3_dsr[11]	43.487	0.153	43.207	43.485	43.781
beta3_dsr[12]	33.972	0.831	32.112	34.114	34.809
beta3_dsr[13]	43.259	0.313	42.849	43.190	43.883
beta3_dsr[14]	43.356	0.242	43.078	43.283	43.963
beta3_dsr[15]	43.510	0.190	43.160	43.509	43.856
beta3_dsr[16]	43.441	0.161	43.164	43.433	43.764
beta4_dsr[11]	0.594	0.220	0.178	0.589	1.025
beta4_dsr[12]	0.244	0.434	-0.655	0.252	1.078
beta4_dsr[13]	-0.161	0.218	-0.581	-0.159	0.266
beta4_dsr[14]	0.150	0.249	-0.354	0.153	0.617
beta4_dsr[15]	0.725	0.206	0.321	0.725	1.148
beta4_dsr[16]	0.151	0.234	-0.306	0.152	0.610
beta0_slope[11]	-1.847	0.146	-2.139	-1.845	-1.572
beta0_slope[12]	-4.479	0.258	-5.007	-4.473	-4.009
beta0_slope[13]	-1.355	0.187	-1.798	-1.342	-1.034
beta0_slope[14]	-2.670	0.163	-2.994	-2.668	-2.351
beta0_slope[15]	-1.344	0.144	-1.624	-1.348	-1.064
beta0_slope[16]	-2.735	0.155	-3.036	-2.736	-2.444
beta1_slope[11]	4.487	0.224	4.057	4.489	4.929
beta1_slope[12]	3.989	0.455	3.086	3.987	4.884
beta1_slope[13]	2.738	0.464	2.217	2.651	4.184
beta1_slope[14]	6.304	0.419	5.505	6.307	7.143
beta1_slope[15]	3.015	0.204	2.624	3.016	3.410
beta1_slope[16]	5.276	0.279	4.726	5.279	5.805
beta2_slope[11]	8.766	2.383	5.167	8.337	14.287
beta2_slope[12]	6.614	2.913	1.218	6.586	12.869
beta2_slope[13]	5.111	2.996	0.371	4.952	11.091
beta2_slope[14]	6.288	2.499	2.207	6.118	11.773
beta2_slope[15]	8.238	2.373	4.512	7.848	13.873
beta2_slope[16]	7.758	2.322	4.307	7.438	13.240
beta3_slope[11]	43.461	0.136	43.214	43.452	43.732
beta3_slope[12]	43.350	0.274	42.905	43.313	43.904
beta3_slope[13]	43.449	0.402	42.893	43.391	44.066
beta3_slope[14]	43.269	0.135	43.094	43.237	43.602
beta3_slope[15]	43.494	0.162	43.193	43.491	43.794
beta3_slope[16]	43.374	0.143	43.147	43.354	43.700
beta4_slope[11]	-0.732	0.164	-1.059	-0.730	-0.407
beta4_slope[12]	-1.163	0.460	-2.165	-1.129	-0.374
beta4_slope[13]	0.090	0.163	-0.226	0.091	0.408
beta4_slope[14]	-0.090	0.195	-0.472	-0.095	0.306
beta4_slope[15]	-0.763	0.158	-1.075	-0.760	-0.464
beta4_slope[16]	-0.160	0.173	-0.498	-0.161	0.171
sigma_H[1]	0.200	0.054	0.103	0.198	0.314
sigma_H[2]	0.172	0.031	0.118	0.170	0.239
sigma_H[3]	0.197	0.044	0.119	0.195	0.289
sigma_H[4]	0.419	0.079	0.290	0.411	0.593
sigma_H[5]	0.993	0.205	0.615	0.981	1.408
sigma_H[6]	0.384	0.206	0.030	0.376	0.817
sigma_H[7]	0.309	0.064	0.210	0.300	0.458
sigma_H[8]	0.418	0.088	0.281	0.409	0.614
sigma_H[9]	0.521	0.122	0.327	0.508	0.787
sigma_H[10]	0.215	0.043	0.139	0.213	0.308
sigma_H[11]	0.277	0.046	0.200	0.273	0.378
sigma_H[12]	0.437	0.164	0.206	0.415	0.767
sigma_H[13]	0.216	0.038	0.152	0.212	0.300
sigma_H[14]	0.508	0.094	0.343	0.501	0.705
sigma_H[15]	0.247	0.039	0.180	0.244	0.332
sigma_H[16]	0.227	0.045	0.152	0.223	0.328
lambda_H[1]	3.186	3.945	0.161	1.873	13.649
lambda_H[2]	8.292	8.037	0.803	5.876	29.702
lambda_H[3]	6.125	9.439	0.275	3.165	30.183
lambda_H[4]	0.006	0.004	0.001	0.005	0.017
lambda_H[5]	3.722	7.788	0.032	1.046	25.164
lambda_H[6]	7.694	15.046	0.009	0.951	50.845
lambda_H[7]	0.013	0.009	0.002	0.011	0.035
lambda_H[8]	8.149	9.805	0.111	4.636	35.178
lambda_H[9]	0.015	0.010	0.003	0.013	0.040
lambda_H[10]	0.321	0.800	0.032	0.199	1.114
lambda_H[11]	0.280	0.416	0.012	0.134	1.335
lambda_H[12]	4.764	5.743	0.200	2.828	21.873
lambda_H[13]	3.422	3.135	0.209	2.560	11.649
lambda_H[14]	3.317	4.122	0.243	2.035	14.666
lambda_H[15]	0.026	0.048	0.003	0.017	0.099
lambda_H[16]	0.901	1.277	0.048	0.474	4.330
mu_lambda_H[1]	4.379	1.874	1.253	4.219	8.400
mu_lambda_H[2]	3.878	1.947	0.633	3.767	8.026
mu_lambda_H[3]	3.539	1.826	0.824	3.269	7.659
sigma_lambda_H[1]	8.687	4.234	2.050	8.135	18.003
sigma_lambda_H[2]	8.458	4.705	1.037	7.861	18.244
sigma_lambda_H[3]	6.258	3.878	1.037	5.452	15.943
beta_H[1,1]	6.957	1.062	4.361	7.109	8.612
beta_H[2,1]	9.874	0.489	8.800	9.892	10.799
beta_H[3,1]	8.011	0.804	6.129	8.102	9.289
beta_H[4,1]	9.477	7.781	-6.178	9.698	24.430
beta_H[5,1]	0.125	2.352	-4.927	0.302	4.230
beta_H[6,1]	3.114	3.885	-6.753	4.464	7.559
beta_H[7,1]	0.457	5.931	-12.277	0.922	11.161
beta_H[8,1]	1.304	3.573	-2.228	1.229	3.423
beta_H[9,1]	12.896	5.772	1.162	12.783	24.348
beta_H[10,1]	7.051	1.710	3.483	7.112	10.298
beta_H[11,1]	5.231	3.472	-2.602	6.006	9.966
beta_H[12,1]	2.595	1.120	0.787	2.526	4.909
beta_H[13,1]	9.025	1.043	6.814	9.131	10.536
beta_H[14,1]	2.204	0.997	0.104	2.207	4.225
beta_H[15,1]	-6.012	3.850	-12.835	-6.290	2.583
beta_H[16,1]	3.431	2.584	-0.766	3.067	10.125
beta_H[1,2]	7.904	0.239	7.421	7.909	8.352
beta_H[2,2]	10.024	0.139	9.750	10.021	10.297
beta_H[3,2]	8.950	0.200	8.549	8.948	9.335
beta_H[4,2]	3.553	1.484	0.785	3.453	6.700
beta_H[5,2]	1.957	0.976	-0.007	1.987	3.786
beta_H[6,2]	5.705	1.031	3.218	5.869	7.316
beta_H[7,2]	2.652	1.127	0.716	2.549	5.085
beta_H[8,2]	3.006	1.029	1.404	3.148	4.214
beta_H[9,2]	3.514	1.089	1.448	3.486	5.794
beta_H[10,2]	8.190	0.347	7.498	8.203	8.871
beta_H[11,2]	9.756	0.627	8.832	9.636	11.166
beta_H[12,2]	3.942	0.383	3.235	3.936	4.698
beta_H[13,2]	9.119	0.263	8.656	9.109	9.640
beta_H[14,2]	4.026	0.358	3.348	4.017	4.780
beta_H[15,2]	11.340	0.703	9.850	11.393	12.628
beta_H[16,2]	4.548	0.794	3.023	4.544	6.103
beta_H[1,3]	8.452	0.242	8.012	8.444	8.959
beta_H[2,3]	10.064	0.119	9.825	10.062	10.300
beta_H[3,3]	9.611	0.166	9.290	9.609	9.946
beta_H[4,3]	-2.480	0.884	-4.195	-2.477	-0.696
beta_H[5,3]	3.849	0.620	2.595	3.844	5.066
beta_H[6,3]	7.962	1.192	6.320	7.613	10.528
beta_H[7,3]	-2.762	0.670	-4.091	-2.755	-1.469
beta_H[8,3]	5.240	0.470	4.654	5.184	6.171
beta_H[9,3]	-2.831	0.728	-4.264	-2.827	-1.425
beta_H[10,3]	8.700	0.283	8.141	8.695	9.285
beta_H[11,3]	8.547	0.283	7.925	8.576	9.033
beta_H[12,3]	5.253	0.321	4.510	5.290	5.763
beta_H[13,3]	8.837	0.177	8.474	8.841	9.172
beta_H[14,3]	5.720	0.280	5.116	5.739	6.221
beta_H[15,3]	10.374	0.323	9.758	10.364	11.008
beta_H[16,3]	6.319	0.616	4.893	6.383	7.305
beta_H[1,4]	8.264	0.175	7.895	8.277	8.575
beta_H[2,4]	10.127	0.123	9.868	10.133	10.344
beta_H[3,4]	10.112	0.165	9.749	10.125	10.408
beta_H[4,4]	11.799	0.440	10.915	11.805	12.648
beta_H[5,4]	5.516	0.758	4.295	5.429	7.338
beta_H[6,4]	7.043	0.878	5.056	7.288	8.256
beta_H[7,4]	8.260	0.355	7.551	8.257	8.942
beta_H[8,4]	6.708	0.236	6.256	6.717	7.117
beta_H[9,4]	7.222	0.488	6.277	7.216	8.216
beta_H[10,4]	7.750	0.242	7.309	7.741	8.246
beta_H[11,4]	9.394	0.197	9.008	9.394	9.776
beta_H[12,4]	7.136	0.210	6.755	7.132	7.561
beta_H[13,4]	9.033	0.139	8.750	9.036	9.298
beta_H[14,4]	7.737	0.215	7.319	7.738	8.165
beta_H[15,4]	9.469	0.230	9.022	9.469	9.924
beta_H[16,4]	9.346	0.243	8.917	9.329	9.858
beta_H[1,5]	8.987	0.144	8.699	8.990	9.271
beta_H[2,5]	10.784	0.096	10.603	10.780	10.982
beta_H[3,5]	10.920	0.170	10.613	10.911	11.261
beta_H[4,5]	8.392	0.455	7.519	8.389	9.324
beta_H[5,5]	5.412	0.577	4.075	5.468	6.399
beta_H[6,5]	8.741	0.644	7.798	8.595	10.281
beta_H[7,5]	6.748	0.343	6.083	6.739	7.440
beta_H[8,5]	8.216	0.212	7.869	8.201	8.629
beta_H[9,5]	8.199	0.474	7.219	8.209	9.119
beta_H[10,5]	10.080	0.232	9.602	10.074	10.516
beta_H[11,5]	11.505	0.229	11.046	11.512	11.942
beta_H[12,5]	8.477	0.197	8.101	8.472	8.882
beta_H[13,5]	10.005	0.128	9.751	10.003	10.252
beta_H[14,5]	9.197	0.226	8.779	9.189	9.652
beta_H[15,5]	11.167	0.247	10.688	11.168	11.663
beta_H[16,5]	9.925	0.182	9.551	9.932	10.258
beta_H[1,6]	10.181	0.187	9.857	10.166	10.584
beta_H[2,6]	11.512	0.109	11.297	11.511	11.726
beta_H[3,6]	10.809	0.162	10.447	10.817	11.104
beta_H[4,6]	12.893	0.814	11.268	12.892	14.472
beta_H[5,6]	5.890	0.608	4.759	5.877	7.105
beta_H[6,6]	8.764	0.644	7.118	8.877	9.728
beta_H[7,6]	9.861	0.572	8.738	9.862	10.951
beta_H[8,6]	9.523	0.278	9.019	9.539	9.979
beta_H[9,6]	8.478	0.786	6.897	8.469	10.046
beta_H[10,6]	9.497	0.327	8.791	9.533	10.055
beta_H[11,6]	10.827	0.350	10.059	10.857	11.448
beta_H[12,6]	9.372	0.244	8.918	9.369	9.880
beta_H[13,6]	11.045	0.165	10.764	11.040	11.376
beta_H[14,6]	9.828	0.288	9.236	9.829	10.387
beta_H[15,6]	10.833	0.431	9.960	10.844	11.643
beta_H[16,6]	10.553	0.236	10.043	10.558	11.024
beta_H[1,7]	10.913	0.834	8.894	11.006	12.282
beta_H[2,7]	12.206	0.433	11.323	12.217	13.039
beta_H[3,7]	10.544	0.669	9.089	10.597	11.678
beta_H[4,7]	2.497	4.153	-5.518	2.487	10.803
beta_H[5,7]	6.431	1.882	3.045	6.362	10.713
beta_H[6,7]	9.568	2.319	5.115	9.531	15.465
beta_H[7,7]	10.499	2.852	5.024	10.517	16.277
beta_H[8,7]	10.976	1.002	9.438	10.923	12.702
beta_H[9,7]	4.485	3.978	-3.315	4.460	12.535
beta_H[10,7]	9.876	1.481	7.278	9.774	13.039
beta_H[11,7]	10.920	1.689	7.769	10.799	14.721
beta_H[12,7]	9.998	0.942	7.907	10.095	11.516
beta_H[13,7]	11.658	0.767	9.919	11.732	12.862
beta_H[14,7]	10.423	0.955	8.463	10.462	12.115
beta_H[15,7]	12.011	2.221	7.695	11.979	16.325
beta_H[16,7]	12.266	1.225	10.217	12.084	15.078
beta0_H[1]	8.628	13.046	-17.979	8.789	33.693
beta0_H[2]	10.682	6.275	-2.276	10.642	23.900
beta0_H[3]	9.906	9.871	-8.841	9.942	29.972
beta0_H[4]	1.140	185.948	-368.783	4.675	372.957
beta0_H[5]	4.132	25.561	-42.633	4.255	55.696
beta0_H[6]	6.638	48.679	-106.279	7.636	103.062
beta0_H[7]	5.663	134.506	-271.995	9.504	275.221
beta0_H[8]	6.608	34.041	-15.903	6.443	33.009
beta0_H[9]	5.600	121.142	-244.753	7.095	255.308
beta0_H[10]	8.515	33.000	-61.608	8.754	76.597
beta0_H[11]	9.308	47.430	-85.364	9.377	109.616
beta0_H[12]	6.995	11.553	-15.339	7.167	29.879
beta0_H[13]	9.711	11.707	-11.632	9.598	31.071
beta0_H[14]	7.027	11.940	-17.013	7.041	29.944
beta0_H[15]	9.076	102.924	-194.945	6.917	217.362
beta0_H[16]	8.361	25.482	-43.926	7.920	62.713